A journey to Alpha Centauri
at an acceleration of 1G would not take nine years.
As I've posted elsewhere in these forums, I worked out what would be involved relativistically in making such a journey, and came up with some fascinating concepts.
First, if you accelerate continuously at 1G (9.8 m/s/s), you will approach c in 354.3 days - 10 days shy of 1 year. Let's call it a year for ease of calculation.
So it will take you a year to get up to c and another year to slow down, meaning that the minimum Earth time for your journey will be at least 2 years.
So a journey to Alpha Centauri would, by our clocks, take about 6 years - 1 year to get up to speed, 4 years to cover the distance, an another year to slow back down at Alpha Centauri. (I know, I'm not factoring in the distance covered during acceleration / deceleration, but let's keep it simple!)
For the crew of the ship, however, the journey would take only slightly more than 2 years - because if they get close enough to c, that 4-year near-light-speed trip will be relativistically time-dilated down to almost nothing. At 0.999999c, 4 years goes by in a few minutes.
This holds true regardless of the objective length of the journey. A trip to Tau Ceti would take around 13 years by our clocks - 1 year speed-up, 11 year travel time, 1 year slow down. But for the crew of the ship, it would still only take 2 years, if you could get the ship close enough to c that that 11 years passes in a few minutes by relativistic time dilation.
The practical upshot of this is that for an interstellar voyage of any length - be it to Alpha Centauri or the far side of the Virgo-Coma Supercluster - the voyage, to the ship's crew, will always be slightly more than two years. Granted, for the latter journey, the Sun will have expanded to a red giant and gutted the Earth by the time they get back; but for them it will still have been only a 4-year cruise.
This is technically achievable with today's technology, with one small problem: accelerating a decently-sized ship at 1G for a whole year (and back down again) is going to suck a whole lot of energy. 1G comes out to about 10J/kg/s, so if we assume a GVM of 10,000 t for the ship, that's 10,000,000 kg x 30612245 s * 10J = 3,061.2 Terajoules of energy, and that's not accounting for the relativity-dilated mass of the ship near the speed of light.
As a comparison, the Earth receives 17,000 Terajoules of energy from the Sun every second, so while the energy requirement for the ship is large, it's not insurmountable. Once we master fusion or even anti-matter-matter reactions, we're on our way to the stars.
Just don't expect anyone you know to still be alive by the time you get back if you take a jaunt to anywhere further than Arcturus!